"Then it looks good to me. Keeping in mind that these don't exactly match standard forms I learned, since we're making them up as we go, and my own intelligence is not at the level where I will pretty reliably spot errors on the first pass. I'm not sure quite why I feel the need to say this - it seems like the sort of thing that should be obvious? - but if I'm the one who makes an error, or it just looks like that, speak up. If you're right, you get to be impressive, and if you're wrong, you need to know which mistake you made."
Keltham keeps prodding the group for a while, dropping hints at needed, until he's pretty sure they've written enough random rules to yield in their combination all the rules of first-order arithmetic except for the induction axiom schema. If anybody from Cheliax brilliantly pulls the induction axiom schema out of their ass, he's going to be sure they're getting it from somewhere; maybe dath ilani geniuses pull that kind of shit at their age but the geniuses of this world are only as smart as him unless they're wearing intelligence headbands.